In the context of the ElGamal signature, the public key is (499, 185, B), where "B" is not known to you. Two packages were sent through the insecure channel as follows: (321, 272, 321) (321, 135, 273) Was there a re-use of the ephemeral key?
Added by Troy W.
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The ephemeral key is part of the signature itself. In the given information, two packages are shown, each with three components. The first component of each package is likely the ephemeral key. Show more…
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Given are two protocols in which the sender's party performs the following operation: Protocol A: y = Ek1(Ekpub,r(x)||H(k2||x)) where x is the message, H is a hash function, E is a symmetric-key encryption algorithm, "||" denotes simple concatenation, k1 and k2 are secret keys which are only known to the sender and the receiver, and kpub,r is a public key of the receiver. Protocol B: y = Ek(Ekpub,r(x)||sigkpr,s(H(x))) where k is a shared secret key only known to the sender and the receiver, kpr,s is a private key of the sender (not shared with the receiver), and kpub,r is a public key of the receiver. (a) For each protocol, provide a step-by-step description (e.g., with an itemized list) of what the receiver does upon reception of y. [kpub,s is a public key of the sender, kpub,r is a public key of the receiver] (b) State whether the following security services are given for each of the two prescribed protocols: - confidentiality - integrity - non-repudiation (preventing an entity from denying previous commitments or actions)
Akash M.
Bob knows that the ElGamal cryptosystem is similar to Diffie-Hellman. To generate the ElGamal keys, Bob selects the cyclic group Z*_p with prime p = 20876441 and generator g = 5 as the public parameters (in decimal). Bob also selects his secret key X between 1 and p-1. The public parameters are p, g, and the value h = g^X mod p, while the private parameter is X. Bob's ElGamal encryption uses a random nonce Y between 1 and p-1 and for a given message M between 1 and p-1, and it outputs a pair of values (C1, C2), so that C1 = g^Y mod p, and C2 = M*(h^Y) mod p. This pair of values is the ciphertext for M with nonce Y (i.e., the ciphertext is a tuple). Also, the value "h^Y mod p" is called the "shared secret" of Bob. Bob's ElGamal decryption receives ciphertext (C1, C2) and his secret key X as input and multiplies C2 with the modular multiplicative inverse of the shared secret. Specifically, if "D = C1^X = g^(X*Y) mod p" is the shared secret, and "E = D^(-1) mod p" is the modular multiplicative inverse of the shared secret, the plaintext is "M = E*C2 mod p". Bob notices that ElGamal encryption is malleable. If the encryption of M3 = 12345 is (C1, C2) = (8698838, 17288353), what is the encryption of M4 = 382695 (all numbers are decimal)? Show all your work.
Adi S.
Users A and B use the Diffie-Hellman key exchange technique with a common prime q = 353 and a primitive root α = 3. i. If user A has private key XA = 97, what is A's public key YA? ii. If user B has private key XB = 233, what is B's public key YB? iii. What is the shared secret key?
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